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M/M/1 : FIFO/ ∞ Model

(a) Given N(t) = n, (n = 0, 1 , 2, .. . . ), the current probability distribution of the remaining time until the next arrival is exponential with parameter λn.

(b) Given N(t) = n, (n = 1, 2, .... ), the current probability distribution of the remaining time until the next service completion is exponential with parameter µn.

(c) Only one birth or death can occur at a time.

In the queueing models, arrival of a customer implies a birth and departed customer implies a death. In queueing system both arrivals and departures take place simultaneously. This makes difference from birth-and-death process. In the following queueing models mean arrival rate and mean service rate are constant.